Rule-based approaches form a subclass of PageFlowCentric approaches.
Rule-based approaches (for example Java Server Faces or JSF) have a central set of rules that state, for each location in the UI, all the paths to other locations.
In JSF, such locations are called views. Each view can be visited by a web browser, and upon such a visit, application code is invoked. Such application code should return an outcome: a string denoting the result of the execution. The rules can then state which outcome leads to which successive view.
This sounds very similar to ActionResponseModels. The difference is that the rules here span several requests---when a request is received, the server tracks which view the browser is at, and computes the next view based upon the combination of the current view and the outcome of executing some business code. Maintaining the knowledge of which view is currently active is done for the programmer.